SSD storage has become very common in the hosting industry. However, it is still a lot more expensive than HDD. For example, with the same hosting price, I can get about double the disk space if that is HDD than SSD. So I just want to ask whether it is worth to spend money to buy shared hosting that offer SSD storage? Should I just stick to the traditional technology, HDD, to get more space?

It is up to the requirement of your websites. If you have big websites that are known to use a lot of disk IO, you definitely should use a shared hosting provider that offers SSD space. However, in my opinion, since you are talking about shared hosting, from my experience, practically all websites use very low disk IO, so you don't really need SSD. Spend the cost to get more storage may be more meaningful for most customers.

If you have a normal website and got a complaint about high IO usage from your provider, there is a high chance that your site is having some problems, and you need to find out the reason. If you are using wordpress, you can consider turn off all plugins and change to another theme, best would be the default theme. If you site is having more than a few thousands ands posts/pages, it is time to start thinking about how to optimize the SQL queries to lower down disk IO and CPU usage

As what other members have mentioned. Typically you don't need to seek for SSD shared hosting service, unless you are running high IO usage application, such as torrent.

However, you should be careful and ask your hosting provider whether they are using a virtual private server (VPS) or a real server. If that is a VPS, it is still better to have SSD storage. I had poor performance with VPS using HDD storage, because of abusing activity of my neighbors (other VPS on the same node)

If you require a lot of disk IO for things like MySQL or a high traffic download server (with a lot of uncacheable hits), you should go with SSD storage.

Disk IO is one of the scarcest resources we can give our clients, so a tradeoff needs to be made between read-latency performance and storage space required.